AN APPARATUS FOR DEMONSTRATING GRADIENT INDEX OPTICAL EFFECTS Jennifer Marie Nierer, John Noe and Harold Metcalf, Laser Teaching Center, Department of Physics and Astronomy, Stony Brook University.
Refraction is the well known optical effect in which light rays moving from one medium to another bend towards or away from a line perpendicular to the boundary between the two media. The amount of bending is given by Snell's law, which involves the velocity of light in the two media through the index of refraction n = c/v. Refraction is obviously important in lens and other optical devices, but also has many other less well-known applications, such as measuring the concentration of chemical solutions, urine analysis, etc. Materials with continuously-varying index of refraction are especially fascinating and have many important applications as well, such as Gradient Index (GRIN) lenses and GRIN optical fibers. GRIN phenomena also occur in nature in mirages and other atmospheric effects.
My work in the Laser Teaching Center has involved creating and studying a device for demonstrating gradient-index optical effects. It consists of a small fishtank which is set up with equal portions of Karo corn syrup (n=1.47) and water (n=1.33). Initially the horizontal boundary between the two media is rather sharply defined, and a laser light beam makes a sharp bend at the transition, according to Snell's law. As time goes by, the boundary becomes more and more diffuse, so that the index of refraction varies smoothly from the top to the bottom of the tank. As a result of the index gradient a laser beam crossing the tank bends in a dramatic downwards arc which has an approximately parabolic shape.
One goal of the project was to measure the evolution of the index profile mixture and the resulting changes to the optical trajectory over a period of weeks. After considering several possible methods involving total internal reflection I decided to use the optical activity of the corn syrup as a measure of the index n. The rotation was measured as a function of depth in the tank using a mounted laser pointer and a rotating polarizer. I hope to use this information to predict the observed trajectories of the light, which were recorded in a digital camera.
Besides my tank studies much of my time was spent in developing a web-based resource about refraction and related optics topics. It includes many excellent web links, some of which describe experiments that are simple enough to be performed in a kitchen with only minimal previous background knowledge in science. It is hoped that this web-resource will inspire many others to attempt their own research projects.
This research was supported by NSF Grant No. Phy 99-12312.